def __build_problem(self):
"""Build the matrix representation of the sampling problem."""
# Set up the mathematical problem
prob = constraint_matrices(self.model, zero_tol=feasibility_tol)
# check if there any non-zero equality constraints
equalities = prob.equalities
b = prob.b
homogeneous = all(np.abs(b) < feasibility_tol)
fixed_non_zero = np.abs(prob.variable_bounds[:, 1]) > feasibility_tol
fixed_non_zero &= prob.variable_fixed
# check if there are any non-zero fixed variables, add them as
# equalities to the stoichiometric matrix
if any(fixed_non_zero):
n_fixed = fixed_non_zero.sum()
rows = np.zeros((n_fixed, prob.equalities.shape[1]))
rows[range(n_fixed), np.where(fixed_non_zero)] = 1.0
equalities = np.vstack([equalities, rows])
var_b = prob.variable_bounds[:, 1]
b = np.hstack([b, var_b[fixed_non_zero]])
homogeneous = False
# Set up a projection that can cast point into the nullspace
nulls = nullspace(prob.equalities)
projection = nulls.dot(nulls.T)
# convert bounds to a matrix and add variable bounds as well
return Problem(equalities=equalities,
b=b,
inequalities=prob.inequalities,
bounds=np.atleast_2d(prob.bounds).T,
variable_fixed=prob.variable_fixed,
variable_bounds=np.atleast_2d(prob.variable_bounds).T,
projection=projection,
homogeneous=homogeneous)
def __build_problem(self) -> Problem:
"""Build the matrix representation of the sampling problem.
Returns
-------
Problem
The matrix representation in the form of a NamedTuple.
"""
# Set up the mathematical problem
prob = constraint_matrices(self.model, zero_tol=self.feasibility_tol)
# check if there any non-zero equality constraints
equalities = prob.equalities
b = prob.b
bounds = np.atleast_2d(prob.bounds).T
var_bounds = np.atleast_2d(prob.variable_bounds).T
homogeneous = all(np.abs(b) < self.feasibility_tol)
fixed_non_zero = np.abs(prob.variable_bounds[:,
1]) > self.feasibility_tol
fixed_non_zero &= prob.variable_fixed
# check if there are any non-zero fixed variables, add them as
# equalities to the stoichiometric matrix
if any(fixed_non_zero):
n_fixed = fixed_non_zero.sum()
rows = np.zeros((n_fixed, prob.equalities.shape[1]))
rows[range(n_fixed), np.where(fixed_non_zero)] = 1.0
equalities = np.vstack([equalities, rows])
var_b = prob.variable_bounds[:, 1]
b = np.hstack([b, var_b[fixed_non_zero]])
homogeneous = False
# Set up a projection that can cast point into the nullspace
nulls = nullspace(equalities)
# convert bounds to a matrix and add variable bounds as well
return Problem(
equalities=shared_np_array(equalities.shape, equalities),
b=shared_np_array(b.shape, b),
inequalities=shared_np_array(prob.inequalities.shape,
prob.inequalities),
bounds=shared_np_array(bounds.shape, bounds),
variable_fixed=shared_np_array(prob.variable_fixed.shape,
prob.variable_fixed,
integer=True),
variable_bounds=shared_np_array(var_bounds.shape, var_bounds),
nullspace=shared_np_array(nulls.shape, nulls),
homogeneous=homogeneous,
)
def __init__(self, model, thinning, seed=None):
self.model = model
self.thinning = thinning
self.n_samples = 0
self.S = create_stoichiometric_matrix(model, array_type='dense')
self.NS = nullspace(self.S)
self.bounds = np.array([[r.lower_bound, r.upper_bound]
for r in model.reactions]).T
self.fixed = np.diff(self.bounds, axis=0).flatten() < 2 * BTOL
self.warmup = None
if seed is None:
self._seed = int(time())
else:
self._seed = seed
# Avoid overflow
self._seed = self._seed % np.iinfo(np.int32).max
def __build_problem(self):
"""Build the matrix representation of the sampling problem."""
# Set up the mathematical problem
prob = constraint_matrices(self.model, zero_tol=self.feasibility_tol)
# check if there any non-zero equality constraints
equalities = prob.equalities
b = prob.b
bounds = np.atleast_2d(prob.bounds).T
var_bounds = np.atleast_2d(prob.variable_bounds).T
homogeneous = all(np.abs(b) < self.feasibility_tol)
fixed_non_zero = np.abs(prob.variable_bounds[:, 1]) > \
self.feasibility_tol
fixed_non_zero &= prob.variable_fixed
# check if there are any non-zero fixed variables, add them as
# equalities to the stoichiometric matrix
if any(fixed_non_zero):
n_fixed = fixed_non_zero.sum()
rows = np.zeros((n_fixed, prob.equalities.shape[1]))
rows[range(n_fixed), np.where(fixed_non_zero)] = 1.0
equalities = np.vstack([equalities, rows])
var_b = prob.variable_bounds[:, 1]
b = np.hstack([b, var_b[fixed_non_zero]])
homogeneous = False
# Set up a projection that can cast point into the nullspace
nulls = nullspace(equalities)
# convert bounds to a matrix and add variable bounds as well
return Problem(
equalities=shared_np_array(equalities.shape, equalities),
b=shared_np_array(b.shape, b),
inequalities=shared_np_array(prob.inequalities.shape,
prob.inequalities),
bounds=shared_np_array(bounds.shape, bounds),
variable_fixed=shared_np_array(prob.variable_fixed.shape,
prob.variable_fixed, integer=True),
variable_bounds=shared_np_array(var_bounds.shape, var_bounds),
nullspace=shared_np_array(nulls.shape, nulls),
homogeneous=homogeneous
)
def add_loopless(model, zero_cutoff=1e-12):
"""Modify a model so all feasible flux distributions are loopless.
In most cases you probably want to use the much faster `loopless_solution`.
May be used in cases where you want to add complex constraints and
objecives (for instance quadratic objectives) to the model afterwards
or use an approximation of Gibbs free energy directions in you model.
Adds variables and constraints to a model which will disallow flux
distributions with loops. The used formulation is described in [1]_.
This function *will* modify your model.
Parameters
----------
model : cobra.Model
The model to which to add the constraints.
zero_cutoff : positive float, optional
Cutoff used for null space. Coefficients with an absolute value smaller
than `zero_cutoff` are considered to be zero.
Returns
-------
Nothing
References
----------
.. [1] Elimination of thermodynamically infeasible loops in steady-state
metabolic models. Schellenberger J, Lewis NE, Palsson BO. Biophys J.
2011 Feb 2;100(3):544-53. doi: 10.1016/j.bpj.2010.12.3707. Erratum
in: Biophys J. 2011 Mar 2;100(5):1381.
"""
internal = [i for i, r in enumerate(model.reactions) if not r.boundary]
s_int = create_stoichiometric_array(model)[:, numpy.array(internal)]
n_int = nullspace(s_int).T
max_bound = max(max(abs(b) for b in r.bounds) for r in model.reactions)
prob = model.problem
# Add indicator variables and new constraints
to_add = []
for i in internal:
rxn = model.reactions[i]
# indicator variable a_i
indicator = prob.Variable("indicator_" + rxn.id, type="binary")
# -M*(1 - a_i) <= v_i <= M*a_i
on_off_constraint = prob.Constraint(rxn.flux_expression -
max_bound * indicator,
lb=-max_bound,
ub=0,
name="on_off_" + rxn.id)
# -(max_bound + 1) * a_i + 1 <= G_i <= -(max_bound + 1) * a_i + 1000
delta_g = prob.Variable("delta_g_" + rxn.id)
delta_g_range = prob.Constraint(delta_g + (max_bound + 1) * indicator,
lb=1,
ub=max_bound,
name="delta_g_range_" + rxn.id)
to_add.extend([indicator, on_off_constraint, delta_g, delta_g_range])
model.add_cons_vars(to_add)
# Add nullspace constraints for G_i
for i, row in enumerate(n_int):
name = "nullspace_constraint_" + str(i)
nullspace_constraint = prob.Constraint(S.Zero, lb=0, ub=0, name=name)
model.add_cons_vars([nullspace_constraint])
coefs = {
model.variables["delta_g_" + model.reactions[ridx].id]: row[i]
for i, ridx in enumerate(internal) if abs(row[i]) > zero_cutoff
}
model.constraints[name].set_linear_coefficients(coefs)
def add_loopless(model, zero_cutoff=1e-12):
"""Modify a model so all feasible flux distributions are loopless.
In most cases you probably want to use the much faster `loopless_solution`.
May be used in cases where you want to add complex constraints and
objecives (for instance quadratic objectives) to the model afterwards
or use an approximation of Gibbs free energy directions in you model.
Adds variables and constraints to a model which will disallow flux
distributions with loops. The used formulation is described in [1]_.
This function *will* modify your model.
Parameters
----------
model : cobra.Model
The model to which to add the constraints.
zero_cutoff : positive float, optional
Cutoff used for null space. Coefficients with an absolute value smaller
than `zero_cutoff` are considered to be zero.
Returns
-------
Nothing
References
----------
.. [1] Elimination of thermodynamically infeasible loops in steady-state
metabolic models. Schellenberger J, Lewis NE, Palsson BO. Biophys J.
2011 Feb 2;100(3):544-53. doi: 10.1016/j.bpj.2010.12.3707. Erratum
in: Biophys J. 2011 Mar 2;100(5):1381.
"""
internal = [i for i, r in enumerate(model.reactions) if not r.boundary]
s_int = create_stoichiometric_matrix(model)[:, numpy.array(internal)]
n_int = nullspace(s_int).T
max_bound = max(max(abs(b) for b in r.bounds) for r in model.reactions)
prob = model.problem
# Add indicator variables and new constraints
to_add = []
for i in internal:
rxn = model.reactions[i]
# indicator variable a_i
indicator = prob.Variable("indicator_" + rxn.id, type="binary")
# -M*(1 - a_i) <= v_i <= M*a_i
on_off_constraint = prob.Constraint(
rxn.flux_expression - max_bound * indicator,
lb=-max_bound, ub=0, name="on_off_" + rxn.id)
# -(max_bound + 1) * a_i + 1 <= G_i <= -(max_bound + 1) * a_i + 1000
delta_g = prob.Variable("delta_g_" + rxn.id)
delta_g_range = prob.Constraint(
delta_g + (max_bound + 1) * indicator,
lb=1, ub=max_bound, name="delta_g_range_" + rxn.id)
to_add.extend([indicator, on_off_constraint, delta_g, delta_g_range])
model.add_cons_vars(to_add)
# Add nullspace constraints for G_i
for i, row in enumerate(n_int):
name = "nullspace_constraint_" + str(i)
nullspace_constraint = prob.Constraint(Zero, lb=0, ub=0, name=name)
model.add_cons_vars([nullspace_constraint])
coefs = {model.variables[
"delta_g_" + model.reactions[ridx].id]: row[i]
for i, ridx in enumerate(internal) if
abs(row[i]) > zero_cutoff}
model.constraints[name].set_linear_coefficients(coefs)
